Borehole stability in naturally fractured rocks with drilling mud intrusion and associated fracture strength weakening:A coupled DFN-DEM approach

Borehole instability in naturally fractured rocks poses significant challenges to drilling.Drilling mud invades the surrounding formations through natural fractures under the difference between the wellbore pressure(P w)and pore pressure(P p)during drilling,which may cause wellbore instability.However,the weakening of fracture strength due to mud intrusion is not considered in most existing borehole stability analyses,which may yield significant errors and misleading predictions.In addition,only limited factors were analyzed,and the fracture distribution was oversimplified.In this paper,the impacts of mud intrusion and associated fracture strength weakening on borehole stability in fractured rocks under both isotropic and anisotropic stress states are investigated using a coupled DEM(distinct element method)and DFN(discrete fracture network)method.It provides estimates of the effect of fracture strength weakening,wellbore pressure,in situ stresses,and sealing efficiency on borehole stability.The results show that mud intrusion and weakening of fracture strength can damage the borehole.This is demonstrated by the large displacement around the borehole,shear displacement on natural fractures,and the generation of fracture at shear limit.Mud intrusion reduces the shear strength of the fracture surface and leads to shear failure,which explains that the increase in mud weight may worsen borehole stability during overbalanced drilling in fractured formations.A higher in situ stress anisotropy exerts a significant influence on the mechanism of shear failure distribution around the wellbore.Moreover,the effect of sealing natural fractures on maintaining borehole stability is verified in this study,and the increase in sealing efficiency reduces the radial invasion distance of drilling mud.This study provides a directly quantitative prediction method of borehole instability in naturally fractured formations,which can consider the discrete fracture network,mud intrusion,and associated weakening of fracture strength.The information provided by the numerical approach(e.g.displacement around the borehole,shear displacement on fracture,and fracture at shear limit)is helpful for managing wellbore stability and designing wellbore-strengthening operations.

Limit equilibrium analysis for rock slope stability using basic Hoek–Brown strength criterion

Hoek–Brown(HB)strength criterion can reflect rock’s inherent failure nature,so it is more suitable for analyzing the stability of rock slopes.However,the traditional limit equilibrium methods are at present only suitable for analyzing the rock slope stability using the linear equivalent Mohr–Coulomb(EMC)strength parameters instead of the nonlinear HB strength criterion.Therefore,a new method derived to analyze directly the rock slope stability using the nonlinear HB strength criterion for arbitrary curve slip surface was described in the limit equilibrium framework.The current method was established based on certain assumptions concerning the stresses on the slip surface through amending the initial normal stressσ0 obtained without considering the effect of inter-slice forces,and it can satisfy all static equilibrium conditions of the sliding body,so the current method can obtain the reasonable and strict factor of safety(FOS)solutions.Compared with the results of other methods in some examples,the feasibility of the current method was verified.Meanwhile,the parametric analysis shows that the slope angleβhas an important influence on the difference of the results obtained using the nonlinear HB strength criterion and its linear EMC strength parameters.Forβ≤45°,both of the results are similar,showing the traditional limit equilibrium methods using the linear EMC strength parameters and the current method are all suitable to analyze rock slope stability,but forβ>60°,the differences of both the results are obvious,showing the actual slope stability state can not be reflected in the traditional limit equilibrium methods,and then the current method should be used.

Application of strength reduction method to dynamic anti-sliding stability analysis of high gravity dam with complex dam foundation

Considering that there are some limitations in analyzing the anti-sliding seismic stability of dam-foundation systems with the traditional pseudo-static method and response spectrum method, the dynamic strength reduction method was used to study the deep anti-sliding stability of a high gravity dam with a complex dam foundation in response to strong earthquake-induced ground action. Based on static anti-sliding stability analysis of the dam foundation undertaken by decreasing the shear strength parameters of the rock mass in equal proportion, the seismic time history analysis was carried out. The proposed instability criterion for the dynamic strength reduction method was that the peak values of dynamic displacements and plastic strain energy change suddenly with the increase of the strength reduction factor. The elasto-plastic behavior of the dam foundation was idealized using the Drucker-Prager yield criterion based on the associated flow rule assumption. The result of elasto-plastic time history analysis of an overflow dam monolith based on the dynamic strength reduction method was compared with that of the dynamic linear elastic analysis, and the reliability of elasto-plastic time history analysis was confirmed. The results also show that the safety factors of the dam-foundation system in the static and dynamic cases are 3.25 and 3.0, respectively, and that the F2 fault has a significant influence on the anti-sliding stability of the high gravity dam. It is also concluded that the proposed instability criterion for the dynamic strength reduction method is feasible.

Influence of heterogeneity on rock strength and stiffness using discrete element method and parallel bond model

The particulate discrete element method(DEM) can be employed to capture the response of rock,provided that appropriate bonding models are used to cement the particles to each other.Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors.Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional(2D) models.In situ rock formations are often heterogeneous,thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis.In situ stress states are basically three-dimensional(3D),and therefore it is important to develop 3D models for this purpose.This paper revisits an earlier experimental study on heterogeneous specimens,of which the relative proportions of weaker material(siltstone) and stronger,harder material(sandstone) were varied in a controlled manner.Using a 3D DEM model with the parallel bond model,virtual heterogeneous specimens were created.The overall responses in terms of variations in strength and stiffness with different percentages of weaker material(siltstone) were shown to agree with the experimental observations.There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations,suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.

Strength and Stability Analysis of Deep Sea Drilling Risers

In order to analyze the influence of vortex-induced vibration on the strength and stability of marine drilling risers, a simplified analytical model was established and a method for calculating vortex-induced dynamic response was developed. A case study indicated that at primary resonance, first-order dynamic displacement response is greater than higher-order mode responses, but the influence of dynamic moment and shearing force of higher-order modes cannot be ignored. The natural fi＇equency of risers decreased sharply with increasing length of the riser, but increased with increasing top tension. Various factors should be considered to avoid vortex-induced vibration in practical application, and the influence of vortex-induced vibration could be estimated by calculating the fatigue lifetime of riser.

Stability analysis of shallow tunnels subjected to seepage with strength reduction theory

Based on strength reduction theory,the stability numbers of shallow tunnels were investigated within the framework of upper and lower bound theorems of limit analysis. Stability solutions taking into account of water seepage were presented and compared with those without considering seepage. The comparisons indicate that the maximum difference does not exceed 3.7%,which proves the present method credible. The results show that stability numbers of shallow tunnels considering seepage are much less than those without considering seepage,and that the difference of stability numbers between considering seepage and without considering seepage increase with increasing the depth ratio. The stability numbers decrease with increasing permeability coefficient and groundwater depth. Seepage has significant effects on the stability numbers of shallow tunnels.

Couple analysis on strength reduction theory and rheological mechanism for slope stability

Considering the rheological properties of rock and soil body,and exploiting the merit of strength reduction technique,a theory of couple analysis is brought forward on the basis of strength reduction theory and rheological properties.Then,the concept and the calculation procedure of the safety factor are established at different time.Making use of finite element software ANSYS,the most dangerous sliding surface of the slope can be obtained through the strength reduction technique.According to the dynamic safety factor based on rheological mechanism,a good forecasting could be presented to prevent and cure the landslide.The result shows that the couple analysis reveals the process of the slope failure with the time and the important influence on the long-term stability due to the rheological parameters.

Quantification of the stiffness and strength of cadherin ectodomain binding with different ions

The stiffness and strength of extracellular （EC） region of cadherin are proposed to be two important mechanical properties both for cadherin as a mechanotransductor and for the formation of cell-cell adhesion. In this study, we quantitatively characterized the stiffness and strength of EC structure when it binds with different types of ions by molecular dynamics simulations. Resuits show that EC structure exhibits a rod-like shape with high stiffness and strength when it binds with the bivalent ions of calcium or magnesium. However, it switches to a soft and collapsed conformation when it binds with the monova- lent ions of sodium or potassium. This study sheds light on the important role of the bivalent ions of calcium in the physiological function of EC.

Upper bound analysis of slope stability with nonlinear failure criterion based on strength reduction technique

Based on the upper bound limit analysis theorem and the shear strength reduction technique, the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its corresponding critical failure mechanism by means of the kinematical approach of limit analysis theory. The nonlinear shear strength parameters were treated as variable parameters and a kinematically admissible failure mechanism was considered for calculation schemes. The iterative optimization method was adopted to obtain the safety factors. Case study and comparative analysis show that solutions presented here agree with available predictions when nonlinear criterion reduces to linear criterion, and the validity of present method could be illuminated. From the numerical results, it can also be seen that nonlinear parameter rn, slope foot gradient ,β, height of slope H, slope top gradient a and soil bulk density γ have significant effects on the safety factor of the slope.

Stability of an explicit time-integration algorithm for hybrid tests, considering stiffness hardening behavior

An explicit unconditionally stable algorithm for hybrid tests,which is developed from the traditional HHT-α algorithm,is proposed.The unconditional stability is first proven by the spectral radius method for a linear system.If the value of α is selected within [-0.5,0],then the algorithm is shown to be unconditionally stable.Next,the root locus method for a discrete dynamic system is applied to analyze the stability of a nonlinear system.The results show that the proposed method is conditionally stable for dynamic systems with stiffness hardening.To improve the stability of the proposed method,the structure stiffness is then identified and updated.Both numerical and pseudo-dynamic tests on a structure with the collision effect prove that the stiffness updating method can effectively improve stability.

Numerical Simulation and Experimental Verification of the Stiffness and Stability of Thrust Pad Aerostatic Bearings

Many researchers concentrate on improving the stiffness and stability of aerostatic bearings, however the contradiction between stiffness and stability is still existed. Therefore, orifice, multiple, and porous restrictors are designed to illustrate the influence of restrictor characteristics on the stability and stiffness of the aerostatic circular pad bearings. Because both the stiffness and stability of aerostatic bearings are determined by the internal pressure distribution, the full Navier?Stokes(N?S) equations are applied to solve internal pressure distribution in bearing film by using computational fluid dynamics(CFD) method. Simulation results present that the stiffness and stability of aerostatic circular pad bearings are influenced significantly by geometrical and material parameters, such as film thickness, orifice diameters, and viscous resistance coe cient. Verified by the experimental data, the micro vibration of orifice restrictor is almost the same as multiple restrictors with amplitude of 0.02 m/s~2, but it is much stronger than the porous restrictors with acceleration of 0.006 m/s~2. The optimal stiffness of multiple restrictors increased by 46%, compared to only 30.2 N/μm of orifice restrictor, and the porous restrictors had obvious advantage in the small film thickness less than 6 μm where the optimal stiffness increased to 38.3 N/μm. The numerical and experimental results provide guidance for improving the stiffness and stability of aerostatic bearings.

Assessment on strength reduction schemes for geotechnical stability analysis involving the Drucker-Prager criterion

For geotechnical stability analysis involving the Drucker-Prager(DP)criterion,both the c-ϕreduction scheme and the M-K reduction scheme can be utilized.With the aid of the second-order cone programming optimized finite element method(FEM-SOCP),a comparison of the two strength reduction schemes for the stability analysis of a homogeneous slope and a multilayered slope is carried out.Numerical investigations disclose that the FoS results calculated by the c-ϕreduction scheme agree well with those calculated by the classical Morgenstern-Price solutions.However,the FoS results attained by the M-K reduction scheme may lead to conservative estimation of the geotechnical safety,particularly for the cases with large internal friction angles.In view of the possible big difference in stability analysis results caused by the M-K reduction scheme,the c-ϕreduction scheme is recommended for the geotechnical stability analyses involving the DP criterion.

Strength and stiffness reduction factors for infilled frames with openings

Framed structures are usually infilled with masonry walls. They may cause a significant increase in both stiffness and strength, reducing the deformation demand and increasing the energy dissipation capacity of the system. On the other hand, irregular arrangements of the masonry panels may lead to the concentration of damage in some regions, with negative effects; for example soft story mechanisms and shear failures in short columns. Therefore, the presence ofinfill walls should not be neglected, especially in regions of moderate and high seismicity. To this aim, simple models are available for solid infills walls, such as the diagonal no-tension strut model, while infilled frames with openings have not been adequately investigated. In this study, the effect of openings on the strength and stiffness of infilled frames is investigated by means of about 150 experimental and numerical tests. The main parameters involved are identified and a simple model to take into account the openings in the infills is developed and compared with other models proposed by different researchers. The model, which is based on the use of strength and stiffness reduction factors, takes into account the opening dimensions and presence of reinforcing elements around the opening. An example of an application of the proposed reduction factors is also presented.

Influences of Randomly Distributed Wall Thickness of Beverage Can on Its Strength and Stiffness

This paper describes the research undertaken on the strength and stiffness of fluctuation on the wall thickness of steel beverage cans using the Monte Carlo stochastic finite element method. Sample distributions were firstly assumed and then proven using the data observations of the wall thickness, the APDL language was then applied, and the stresses and displacements of the can were calculated by using the ANSYS software. It is concluded that the structural reliability of a steel making beverage can be estimated accurately.

Two-dimensional face stability analysis in rock masses governed by the Hoek-Brown strength criterion with a new multi-horn mechanism

The face stability problem is a major concern for tunnels excavated in rock masses governed by the Hoek-Brown strength criterion.To provide an accurate prediction for the theoretical solution of the critical face pressure,this study adopts the piecewise linear method(PLM)to account for the nonlinearity of the strength envelope and proposes a new multi-horn rotational mechanism based on the Hoek-Brown strength criterion and the associative flow rule.The analytical solution of critical support pressure is derived from the energy-work balance equation in the framework of the plastic limit theorem;it is formulated as a multivariable nonlinear optimization problem relying on 2m dependent variables(m is the number of segments).Meanwhile,two classic linearized measures,the generalized tangential technique(GTT)and equivalent Mohr-Coulomb parameters method(EMM),are incorporated into the analysis for comparison.Surprisingly,the parametric study indicates a significant improvement in support pressure by up to 13%compared with the GTT,and as expected,the stability of the tunnel face is greatly influenced by the rock strength parameters.The stress distribution on the rupture surface is calculated to gain an intuitive understanding of the failure at the limit state.Although the limit analysis is incapable of calculating the true stress distribution in rock masses,a rough approximation of the stress vector on the rupture surface is permitted.In the end,sets of normalized face pressure are provided in the form of charts for a quick assessment of face stability in rock masses.

Seismic stability safety evaluation of gravity dam with shear strength reduction method

A new method of numerical seismic stability safety evaluation for a rock slope is proposed based on the analysis of a gravity dam foundation subjected to earthquake loading. The shear strengths of the weak discontinuities are divided by different shear strength reduction ratios （K） and numerical seismic analysis is carried out after the static analysis is completed. With different K values, the curves of the permanent horizontal displacement of key points of the dam foundation （K-displacement curves） are studied. According to the curve change, the distribution of plastic zones in the foundation, and the slow convergence of the finite element method （FEM）, the seismic stability safety factor is defined as Kwhen the gravity dam is in the limit equilibrium state subjected to earthquake loading. These concepts were applied to the evaluation of seismic stability safety of a gravity dam for a hydropower project. The analysis of the example shows that the proposed method is feasible and is an effective method of seismic stability safety evaluation.

Influence of particle size and ionic strength on the freeze-thaw stability of emulsions stabilized by whey protein isolate

The influence of particle size and ionic strength on the freeze-thaw(FT) stability of emulsions stabilized by whey protein isolate(WPI) was investigated in this study. The destabilization of emulsions during the FT process could be suppressed in a way by decreasing the particle size of the initial emulsions, which was the result of retarding the coalescence between oil droplets. To further improve the FT stability of emulsions, different amounts of Na Cl were added before emulsification. The emulsions with the ionic strength at 30–50 mmol/L exhibited good FT stability. Notably, the ionic strength in this range would not lower the freezing point of emulsions below the freezing temperature used in this study. Salt addition could improve the structural properties of proteins, which was available to strengthen the rigidity and thickness of interfacial layers, sequentially building up the resistance that the destruction of ice crystals to emulsions. Moreover, stronger flocculation between emulsion droplets could promote the formation of a gel-like network structure dominated by elasticity in the emulsion system, which might effectively inhibit the movement of droplets, and improve the FT stability of emulsions eventually. The result was of great significance for the preparation of emulsion-based foods with improved FT stability.

Vane Shear Strength Based Stability Analysis of Slopes in Unconsolidated Soft Clay

In-situ vane shear test is frequently performed to determine shear strength for slope stability analysis in Tianjin New Harbor.However,the soil shear strength varies with the shear plane orientation.A possible means to reduce the effect of directional dependency of shear strength is to convert the in-situ vane shear strength into undrained shear strength parameters.A method of converting in-situ vane shear strength into undrained shear strength parameters is presented.The shear strength parameters determined for all of the in-situ vane shear strengths are subjected to statistical regression analysis to take into consideration the possible effect of non-homogeneity in the soft clay deposit.Using the regressed shear strength parameters,slope stability analyses are performed for five existing soil slopes.The results of stability analyses indicate that the safety factors obtained from the converted parameters reflect the state of the slopes analyzed much better than those obtained from in-situ vane shear strength and laboratory consolidated-undrained and unconsolidated-undrained strength parameters.It is concluded that the presented methsod of determining undrained shear strength parameters for in-situ vane shear strength is effective.

Limit equilibrium method(LEM) of slope stability and calculation of comprehensive factor of safety with double strength-reduction technique

When the slope is in critical limit equilibrium(LE) state, the strength parameters have different contribution to each other on maintaining slope stability. That is to say that the strength parameters are not simultaneously reduced. Hence, the LE stress method is established to analyze the slope stability by employing the double strengthreduction(DSR) technique in this work. For calculation model of slope stability under the DSR technique, the general nonlinear Mohr–Coulomb(M–C) criterion is used to describe the shear failure of slope. Meanwhile, the average and polar diameter methods via the DSR technique are both adopted to calculate the comprehensive factor of safety(FOS) of slope. To extend the application of the polar diameter method, the original method is improved in the proposed method. After comparison and analysis on some slope examples, the proposed method's feasibility is verified. Thereafter, the stability charts of slope suitable for engineering application are drawn. Moreover, the studies show that:(1) the average method yields similar results as that of the polardiameter method;(2) compared with the traditional uniform strength-reduction(USR) technique, the slope stability obtained using the DSR techniquetends to be more unsafe; and(3) for a slope in the critical LE state, the strength parameter φ, i.e., internal friction angle, has greater contribution on the slope stability than the strength parameters c, i.e., cohesion.

An Application of the Modified Shear Lag Model to Study the Influence of Thermal Residual Stresses on the Stiffness and Yield Strength of Short Fiber Reinforced Metal Matrix Composites

The modified shear lag model proposed recently was applied to calculate thermal residual stresses and subsequent stress distributions under tensile and compressive loadings. The expressions for the elastic moduli and the yield strengths under tensile and compressive loadings were derived which take account of thermal residual stresses. The asymmetries in the elastic modulus and the yield strength were interpreted using the derived expressions and the obtained results of the stress calculations. The model predictions have exhibited good agreements with the experimental results and also with the other theoretical predictions